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%I #25 Dec 30 2024 04:25:26
%S 0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,
%T 0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,
%U 1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1
%N An infinite sequence over {0,1} with no palindromes of length > 12.
%C A palindrome is a block that reads the same forwards and backwards.
%H Kevin Ryde, <a href="/A372258/b372258.txt">Table of n, a(n) for n = 0..10000</a>
%H Jean Berstel, Luc Boasson, Olivier Carton, and Isabelle Fagnot, <a href="https://arxiv.org/abs/0903.2382">Infinite words without palindrome</a>, arXiv:0903.2382 [cs.DM], March 13 2009, section 3 word "z".
%F Generated by iterating the morphism 0->01, 1->21, 2->34, 3->01, 4->54, 5->34, followed by the coding n->n mod 2.
%F From _Kevin Ryde_, Apr 28 2024: (Start)
%F a(n) = A372257(n) mod 2.
%F a(n) = (n + A014707(floor(n/2))) mod 2 [per Berstel et al section 4, but misprint there "word y" should be "word z"]. (End)
%F First difference, taken modulo 2, of the paperfolding sequence with unfolding instructions 001111.... . - _Jeffrey Shallit_, Dec 29 2024
%o (PARI) a(n) = bitxor(bitand(n,1), bittest(n, valuation(n>>1+1,2)+2)); \\ _Kevin Ryde_, Apr 28 2024
%Y Cf. A014707, A369989, A372257.
%K nonn,easy
%O 0
%A _Jeffrey Shallit_, Apr 24 2024